Pretty nice. I am not sure if you can get a full carpet with no CO2 or ferts. Reason being, carpet plants are fragile and poor competitors. Those stem plants will take most if not all the available CO2 and nutrients. Maybe you should look into DIY CO2 atleast. I have tried doing it on 2 tanks before and didn't work out. I went with an easier carpet plant still waiting on the results. But I also made some adjustments in my tanks too, that hopefully help.
As for the carpet, the Parvula supposedly requires hardly anything to grow. While i'll agree it won't be superb without additives, i believe it can be done without, and still be pleasing to look at.
I wouldn't mind adding some Carbon through a liquid, but as long as there is no need to, i won't. If it aint broke don't fix it But ofc, if it turns out i will need heavyer fertilization and Carbon, i will ofcourse supply the tank with it.
I'm actually surprised that the Alternanthera reineckii can look this good under these conditions.